Abstract
Modelling the dynamic dependent data by the linear approach is the most popular among the researchers because of its simplicity in calculation and approximation, however, in real-world phenomena, most of the time-dependent data follow the nonlinearity. Moreover, most of the nonlinear modelling of time-dependent data have found in the financial applications. Besides this sector, the authors of this paper found the presence of nonlinearity in meteorological data with the help of four popular nonlinearity tests. Furthermore, there is a scarcity of the application of regime-switching threshold autoregressive nonlinear time-series model in forecasting the weather variables like temperature. Thus, this paper aims to compare the forecasting accuracy of the linear autoregressive (linear AR), self-exciting threshold autoregression (SETAR), logistic smooth transition autoregressive model (LSTAR), and feed-forward neural network (ANNs) and fitted with the determination of regime and hyperparameters. After fitting the models, twenty steps ahead forecast considered for the comparison along with the selected model selection criteria; and results depict that the LSTAR models are selected as the most appropriate fitted models for forecasting the daily Average, Maximum and Minimum temperature. Finally, it has observed that the average, as well as maximum temperature of Dhaka, Bangladesh, have an increasing trend and minimum temperature having a decreasing trend.
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References
Acatrinei MC, Caraiani P (2011) Modeling and forecasting the dynamics in romanian stock market indices using threshold models. Roman J Econ Forecast 14(2):42–54
Allen S, Ferro CAT, Kwasniok F (2020) Recalibrating wind speed forecasts using regime-dependent ensemble model output statistics. Q J R Meteorol Soc. https://doi.org/10.1002/qj.3806
Antwi E, Gyamfi EN, Kyei KA (2019) Modeling and forecasting Ghana’s inflation rate under threshold models. J Dev Areas. https://doi.org/10.1353/jda.2019.0040
Aydin D, Güneri Öİ (2015) Time series prediction using hybridization of AR, SETAR and ARM models. Int J Appl 5(6):87–96
Boero G, Lampis F (2017) The forecasting performance of setar models: an empirical application. Bull Econ Res 69(3):216–228. https://doi.org/10.1111/boer.12068
Boero G, Marrocu E (2002) The performance of non-linear exchange rate models: a forecasting comparison. J Forecast 21(7):513–542. https://doi.org/10.1002/for.837
Bradley MD, Jansen DW (2004) Forecasting with a nonlinear dynamic model of stock returns and industrial production. Int J Forecast 20(2):321–342. https://doi.org/10.1016/j.ijforecast.2003.09.007
Bratčikovienė N (2012) Adapted SETAR model for lithuanian HCPI time series. Nonlinear Anal Model Control 17(1):27–46. https://doi.org/10.15388/NA.17.1.14076
Brock WA (1987) A test for independence based on the correlation dimension. University of Wisconsin-Madison, Social Systems Research Institute, Wisconsin
Broock WA, Scheinkman JA, Dechert WD, LeBaron B (1996) A test for independence based on the correlation dimension. Econom Rev 15(3):197–235. https://doi.org/10.1080/07474939608800353
Chan KS, Tsay RS (1998) Limiting properties of the least squares estimator of a continuous threshold autoregressive model. Biometrika 85(2):413–426. https://doi.org/10.1093/biomet/85.2.413
Chen D, Bunn D (2014) The forecasting performance of a finite mixture regime-switching model for daily electricity prices. J Forecast 33(5):364–375
Chu F-L (2008) A fractionally integrated autoregressive moving average approach to forecasting tourism demand. Tour Manag 29(1):79–88. https://doi.org/10.1016/j.tourman.2007.04.003
Clements MP, Smith J (1999) A Monte Carlo study of the forecasting performance of empirical SETAR models. J Appl Econom 14(2):123–141
Clements MP, Smith J (2001) Evaluating forecasts from SETAR models of exchange rates. J Int Money Finance 20(1):133–148. https://doi.org/10.1016/S0261-5606(00)00039-5
Dacco R, Satchell S (1999) Why do regime-switching models forecast so badly? J Forecast 18(1):1–16
Engle RF (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom Inflation. Econom: J Econom Soc 50:987–1007. https://doi.org/10.2307/1912773
Feng H, Liu J (2003) A SETAR model for Canadian GDP: non-linearities and forecast comparisons. Appl Econ 35(18):1957–1964. https://doi.org/10.1080/0003684032000160674
Franses PH, Franses RFPH, van Dijk D (2000) Non-linear time series models in empirical finance. Cambridge University Press, Cambridge
Gonzalo J, Pitarakis J-Y (2002) Estimation and model selection based inference in single and multiple threshold models. J Econom 110(2):319–352. https://doi.org/10.1016/S0304-4076(02)00098-2
Haldrup N, Nielsen MØ (2006) A regime switching long memory model for electricity prices. J Econom 135(1–2):349–376
Bruce E. Hansen (1997) Inference in TAR models. Unpublished working paper. Boston College Department of Economics, Chestnut Hill
Ismail MT, Isa Z (2006) Modelling exchange rates using regime switching models. Sains Malaysiana 35(2):55–62
Janczura J, Weron R (2010) An empirical comparison of alternate regime-switching models for electricity spot prices. Energy Econ 32(5):1059–1073
Keenan DM (1985) A Tukey nonadditivity-type test for time series nonlinearity. Biometrika 72(1):39–44. https://doi.org/10.1093/biomet/72.1.39
Kräger H, Kugler P (1993) Non-linearities in foreign exchange markets: a different perspective. J Int Money Finance 12(2):195–208. https://doi.org/10.1016/0261-5606(93)90024-6
la Torre-Torres D, Oscar V, Galeana-Figueroa E, Álvarez-García J (2020) A test of using markov-switching GARCH models in oil and natural gas trading. Energies 13(1):129
Lerch S, Thorarinsdottir TL (2013) Comparison of non-homogeneous regression models for probabilistic wind speed forecasting. Tellus A: Dyn Meteorol Oceanogr 65(1):21206
Luukkonen R, Saikkonen P, Teräsvirta T (1988) Testing linearity against smooth transition autoregressive models. Biometrika 75(3):491–499. https://doi.org/10.1093/biomet/75.3.491
McLeod AI, Li WK (1983) Diagnostic checking arma time series models using squared-residual autocorrelations. J Time Ser Anal 4(4):269–273. https://doi.org/10.1111/j.1467-9892.1983.tb00373.x
Montgomery AL, Zarnowitz V, Tsay RS, Tiao GC (1998) Forecasting the U.S. Unemployment Rate. J Am Stat Assoc 93(442):478–493. https://doi.org/10.1080/01621459.1998.10473696
Narzo AFD, Aznarte JL, Stigler M, Tsung-wu H (2020) tsDyn: nonlinear time series models with regime switching. Version 10-1.1. https://CRAN.R-project.org/package=tsDyn
Olson DL, Wu DD (2020) Predictive data mining models, 2nd edn. Springer, Singapore
Oscar V, Aguilasocho-Montoya D, Álvarez-García J, Simonetti B (2020) Using Markov-switching models with Markov chain Monte Carlo inference methods in agricultural commodities trading. Soft Comput 1–14
Ouyang T, Huang H, He Y, Tang Z (2020) Chaotic wind power time series prediction via switching data-driven modes. Renew Energy 145:270–281
Potter SM (1995) A nonlinear approach to US GNP. J Appl Econom 10(2):109–125. https://doi.org/10.1002/jae.3950100203
Potter S (1999) Nonlinear time series modelling: an introduction. J Econ Surv 13(5):505–528. https://doi.org/10.1111/1467-6419.00096
Ramsey JB (1969) Tests for specification errors in classical linear least-squares regression analysis. J R Stat Soc: Ser B (Methodol) 31(2):350–371. https://doi.org/10.1111/j.2517-6161.1969.tb00796.x
Reikard G (2010) Regime-switching models and multiple causal factors in forecasting wind speed. Wind Energy 13(5):407–418
Rothman P (1998) Forecasting asymmetric unemployment rates. Rev Econ Stat 80(1):164–168. https://doi.org/10.1162/003465398557276
Sarantis N (1999) Modeling non-linearities in real effective exchange rates. J Int Money Finance 18(1):27–45. https://doi.org/10.1016/S0261-5606(98)00045-X
Skalin J, Teräsvirta T (1999) Another look at Swedish business cycles, 1861–1988. J Appl Econom 14(4):359–378
Song Z, Jiang Y, Zhang Z (2014) Short-term wind speed forecasting with Markov-switching model. Appl Energy 130:103–112
Teräsvirta T (1994) Specification, estimation, and evaluation of smooth transition autoregressive models. J Am Stat Assoc 89(425):208–218. https://doi.org/10.1080/01621459.1994.10476462
Teräsvirta T (1996) Modelling economic relationships with smooth transition regressions. Stockholm School of Economics, Stockholm
Teräsvirta T (1998) Modeling economic relationships with smooth transition regressions. Stockholm School of Economics, Stockholm
Teräsvirta T (2006) Chapter 8 Forecasting economic variables with nonlinear models. In: Elliott G, Granger CWJ, Timmerm ANNs A (eds) Handbook of economic forecasting. Elsevier, pp 413–457
Teräsvirta T, Tjøstheim DWJ, Granger C (1994) Chapter 48 aspects of modelling nonlinear time series. In: Handbook of econometrics. Elsevier, Amsterdam, pp 2917–2957
Teräsvirta T, van Dijk D, Medeiros MC (2005) Linear models, smooth transition autoregressions, and neural networks for forecasting macroeconomic time series: A re-examination. Int J Forecast 21(4):755–774. https://doi.org/10.1016/j.ijforecast.2005.04.010
Tiao GC, Tsay RS (1994) Some advances in non-linear and adaptive modelling in time-series. J Forecast 13(2):109–131. https://doi.org/10.1002/for.3980130206
Tong H (1978) On a threshold model. In: Chen C (ed) Pattern recognition and signal processing. Sijthoff & Noordhoff, Dordrecht, pp 575–586
Tong H (1990) Non-linear time series: a dynamical system approach. Oxford University Press, Oxford
Tong H, Yeung I (1991) On tests for self-exciting threshold autoregressive-type non-linearity in partially observed time series. J R Stat Soc: Ser C (Appl Stat) 40(1):43–62. https://doi.org/10.2307/2347904
Tsay RS (1986) Nonlinearity tests for time series. Biometrika 73(2):461–466. https://doi.org/10.1093/biomet/73.2.461
Tsay RS (2010) Analysis of financial time series. Wiley, New York
Tsay RS, Chen R (2018) Nonlinear time series analysis. Wiley, New York
Tseng Y-T, Kawashima S, Kobayashi S, Takeuchi S, Nakamura K (2020) Forecasting the seasonal pollen index by using a hidden Markov model combining meteorological and biological factors. Sci Total Environ 698:134246
Umer UM, Sevil T, Sevil G (2018) Forecasting performance of smooth transition autoregressive (STAR) model on travel and leisure stock index. J Finance Data Sci 4(2):90–100. https://doi.org/10.1016/j.jfds.2017.11.006
van Dijk D, Teräsvirta T, Franses PH (2002) Smooth transition autoregressive models—A survey of recent developments. Econom Rev 21(1):1–47. https://doi.org/10.1081/ETC-120008723
White H (2006) Chapter 9 approximate nonlinear forecasting methods. In: Elliott G, Granger CWJ, Timmerm ANNs A (eds) Handbook of economic forecasting. Elsevier, Amsterdam, pp 459–512
Acknowledgement
The authors would like to sincerely thank the two anonymous reviewers, the Executive Editor-in-Chief for their valuable comments which is helpful to improve the quality as well as readability of the paper. The authors are thankful to the Bangladesh Meteorological Department, Bangladesh for providing the data for research. The authors also grateful to their family and all well-wishers for motivation, inspiration, and supports to complete this research.
Funding
The authors do not receive any form of financial support from any organization and individuals. They purchased the required dataset from the Bangladesh Meteorological Department, Bangladesh and complete this research by their self-resources.
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Karimuzzaman, M., Moyazzem Hossain, M. Forecasting performance of nonlinear time-series models: an application to weather variable. Model. Earth Syst. Environ. 6, 2451–2463 (2020). https://doi.org/10.1007/s40808-020-00826-6
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DOI: https://doi.org/10.1007/s40808-020-00826-6